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arxiv: 2607.01015 · v1 · pith:Y242TGS7new · submitted 2026-07-01 · 💻 cs.CV

SuperFlex: Deformable Superquadrics for Point Cloud Decomposition

Gabriel Tavernini , Elisabetta Fedele , Tiago Novello , Leonidas Guibas , Marc Pollefeys , Francis Engelmann This is my paper

Pith reviewed 2026-07-02 13:58 UTC · model grok-4.3

classification 💻 cs.CV
keywords superquadricspoint cloud decompositiondeformable primitives3D shape representationpartial point cloudsreconstruction accuracy
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The pith

Superquadrics gain bending, tapering and a new loss to represent curved shapes more accurately in point clouds.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

SuperFlex improves superquadric decompositions of 3D point clouds by introducing a novel loss for higher accuracy. It adds bending and tapering deformations to capture curved and asymmetric shapes that rigid primitives miss. The improved decompositions serve as supervision to train a model that handles partial, real-world scans. This yields substantially better reconstruction accuracy than previous optimization and learning methods while using a compact set of primitives.

Core claim

The framework adds a novel loss formulation and bending and tapering deformations to superquadrics, enabling high-fidelity representation of curved and asymmetric geometries, and leverages these decompositions to train a model robust to partial point clouds.

What carries the argument

Deformable superquadric primitives equipped with bending and tapering, optimized under a new loss function.

Load-bearing premise

The new loss formulation and bending/tapering deformations can be optimized or learned while preserving the geometric interpretability and compactness of the superquadric primitives.

What would settle it

Running the optimization or training on benchmark datasets and measuring no gain in reconstruction metrics such as Chamfer distance over baselines would disprove the accuracy improvements.

Figures

Figures reproduced from arXiv: 2607.01015 by Elisabetta Fedele, Francis Engelmann, Gabriel Tavernini, Leonidas Guibas, Marc Pollefeys, Tiago Novello.

Figure 1
Figure 1. Figure 1: 3D Object Decomposition with Deformable Superquadrics. [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Illustration of superquadric deformations: tapering (red) and bending (blue). Both deformations are shown along a single axis (the z-axis). For tapering along z, the parameters are τx (shown) and τy (not shown). For bending, we select a bending angle αz around the z axis, and bend to the curvature defined by kz [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Illustration of the SuperFlex model. Given an input point cloud, SuperFlex decomposes the object into a set of superquadric primitives, each defined by its pose (t, R), shape (s, ϵ), and deformations (τ , β). The model is trained via self-supervised joint volumetric and surface losses. A subsequent (optional) object-specific optimization can further improve the superquadric decomposition quality using the … view at source ↗
Figure 4
Figure 4. Figure 4: Qualitative Results on ShapeNet. Top row: input point clouds. Below: the outputs of baselines and our methods. Different colors indicate different primitives. For SuperFlex, we compare variants with and without tapering and bending (T&B) deformation parameters. Test-time Opt. IoU↑ F [18]↑ L1↓ L2↓ # Primitives↓ Runtime↓ ✗ 0.72 0.37 1.54 0.043 5.64 0.0082 s ✓ 0.87 0.49 1.32 0.036 5.64 5 s [PITH_FULL_IMAGE:f… view at source ↗
Figure 5
Figure 5. Figure 5: Qualitative Test-time Optimization Results. [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Qualitative Results on ASE. Top row: partial input point clouds. Below: the outputs of our standard SuperFlex and its robust fine-tuned variant. 5.3 Partial Point Clouds Datasets. We evaluate reconstruction under realistic sensing conditions using both quantitative and qualitative experiments. For quantitative evaluation, we use the Aria Synthetic Environments (ASE) dataset [23], while qualitative re￾sults… view at source ↗
Figure 7
Figure 7. Figure 7: Robustness on real-world point clouds. We show results from two Scan￾Net++ scenes where objects are decomposed into sets of superquadrics by our robust SuperFlex variant. Different colors indicate different object instances. A rendering of the original scene is shown in the top-left corner. Qualitative Evaluation [PITH_FULL_IMAGE:figures/full_fig_p013_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Robustness in real-world point clouds. We show four example scene from ScanNet++ where each object is decomposed into a set of superquadrics [PITH_FULL_IMAGE:figures/full_fig_p023_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Robustness in real-world point clouds. We show four examples scene from Replica where each object is decomposed into a set of superquadrics [PITH_FULL_IMAGE:figures/full_fig_p024_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Qualitative Results on ShapeNet. Top row: input point clouds. Below: the outputs of baselines and our methods. Different colors indicate different primitives. For SuperFlex, we compare variants with and without tapering and bending (T&B) deformation parameters [PITH_FULL_IMAGE:figures/full_fig_p026_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Qualitative results on ABO. In each block, the first row shows the input point clouds, the second row shows the direct predictions of SuperFlex, and the third row shows the corresponding optimized results. Different colors denote different primitives [PITH_FULL_IMAGE:figures/full_fig_p027_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Additional Qualitative Results on ShapeNet. [PITH_FULL_IMAGE:figures/full_fig_p028_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: SuperFlex from a single RGB Image. From an input RGB frame, we first compute instance point maps using SAM3 and MoGE. Then, we apply SuperFlex on top of each object’s point map [PITH_FULL_IMAGE:figures/full_fig_p028_13.png] view at source ↗
read the original abstract

Superquadrics have proven to provide a compact, geometrically meaningful representation for 3D objects. However, existing methods suffer from limited reconstruction accuracy, are restricted to rigid primitives, and lack robustness to partial point clouds. In this work, we present SuperFlex, an enhanced framework that expands the expressive power and applicability of superquadric decompositions. First, we introduce a novel loss formulation which significantly improves reconstruction accuracy. Second, we include bending and tapering deformations, enabling high-fidelity representation of curved and asymmetric geometries. Finally, we leverage these high-quality decompositions as supervision to train a model that is robust to partial real-world point clouds. Experiments demonstrate substantial improvements in reconstruction accuracy over both optimization- and learning-based baselines while maintaining a highly compact primitive representation.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper introduces SuperFlex, a framework extending superquadric decomposition of point clouds via a novel loss formulation for improved accuracy, bending and tapering deformations to handle curved and asymmetric shapes, and supervision from these decompositions to train a model robust to partial real-world point clouds. It claims substantial reconstruction accuracy gains over optimization- and learning-based baselines while preserving a compact primitive representation.

Significance. If the quantitative results and ablations hold, the work meaningfully extends the utility of geometrically interpretable superquadrics to more complex real-world geometries and partial observations, potentially benefiting downstream tasks in 3D vision that value both compactness and fidelity over black-box alternatives.

major comments (2)
  1. [Experiments] Experiments section: the central claim of 'substantial improvements' over baselines requires explicit reporting of metrics (e.g., Chamfer distance, IoU), ablation tables isolating the novel loss versus deformations, and error analysis on partial clouds; without these the accuracy claim remains unverified from the abstract alone.
  2. [Method] Method, deformation parameterization: the bending and tapering extensions must be shown not to inflate the effective degrees of freedom beyond the claimed compactness (e.g., via a table of primitive parameter counts before/after deformation); otherwise the interpretability advantage over general meshes is at risk.
minor comments (2)
  1. [Abstract] Abstract, paragraph 2: the phrase 'highly compact primitive representation' would benefit from a concrete comparison (e.g., average number of primitives or bits per shape) to prior superquadric methods.
  2. [Related Work] Related work: ensure explicit citation of the specific superquadric fitting losses used as baselines so readers can assess novelty of the proposed formulation.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thoughtful and constructive feedback. We address each major comment below and commit to revisions that strengthen the experimental reporting and method clarity while preserving the core contributions of the work.

read point-by-point responses

  1. Referee: [Experiments] Experiments section: the central claim of 'substantial improvements' over baselines requires explicit reporting of metrics (e.g., Chamfer distance, IoU), ablation tables isolating the novel loss versus deformations, and error analysis on partial clouds; without these the accuracy claim remains unverified from the abstract alone.

    Authors: The full manuscript reports quantitative results using Chamfer distance and related metrics against both optimization- and learning-based baselines. However, we agree that dedicated ablation tables and partial-cloud error analysis would make the contributions of the novel loss and deformations more transparent. We will add these elements to the experiments section in the revised version. revision: yes

  2. Referee: [Method] Method, deformation parameterization: the bending and tapering extensions must be shown not to inflate the effective degrees of freedom beyond the claimed compactness (e.g., via a table of primitive parameter counts before/after deformation); otherwise the interpretability advantage over general meshes is at risk.

    Authors: We will include a new table in the method section that enumerates the parameter count per primitive for the base superquadric formulation versus the version augmented with bending and tapering. This will explicitly demonstrate that the added deformation parameters remain small in number relative to the gain in expressiveness, thereby preserving the compactness and geometric interpretability of the representation. revision: yes

Circularity Check

0 steps flagged

No significant circularity

full rationale

The available text consists only of the abstract, which states high-level contributions (novel loss, bending/tapering deformations, supervision for partial clouds) without any equations, parameter definitions, loss formulations, or derivation steps. No claimed prediction, uniqueness theorem, or first-principles result is present that could reduce to fitted inputs or self-citations by construction. The experimental claim of improved accuracy is asserted but not supported by any inspectable chain, so no circularity of any enumerated kind can be exhibited. The paper is therefore self-contained against external benchmarks from the given material.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only input supplies no explicit free parameters, axioms, or invented entities; full text required for ledger.

pith-pipeline@v0.9.1-grok · 5672 in / 1031 out tokens · 27398 ms · 2026-07-02T13:58:44.377554+00:00 · methodology

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Reference graph

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